In an automobile assembly line, a work area is used where travelling carriers loaded with vehicle bodies are moved at a constant low operating speed with respective work floors thereof being continuous in a moving direction and at the same time required operations are performed on the loaded vehicle bodies. On the occasion when variable-moving-speed and self-propelled travelling carriers are used in such a work area, the travelling carriers are driven at a high speed except for the above-described work area, whereby the number of necessary travelling carriers in the entire equipment can be reduced and conveyance efficiency in the moving path except for the work area can be increased. In that case, a rear travelling carrier needs to be automatically controlled to decelerate such that the rear travelling carrier approaching the work area at a high speed is decelerated with respect to a front travelling carrier moving near an entrance of the work area at an operating speed and the moving speed of the rear travelling carrier is exactly reduced to the above-described operating speed when the rear travelling carrier is docked with the front travelling carrier. A known deceleration control method applicable to such a case is, although prior art documents thereof cannot be disclosed, such that a distance with the front travelling carrier is detected by a distance sensor and the rear travelling carrier is decelerated based on information about the detected distance with the front travelling carrier.